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Calculation of $6j$-symbols for the Lie algebra $\mathfrak{gl}_n$ (2405.05628v3)
Published 9 May 2024 in math.RT, math-ph, math.CV, and math.MP
Abstract: An explicit description of the multiplicity space that describes occurrences of irreducible representations in a splitting of a tensor product of two irreducible representations of $\mathfrak{gl}_n$ is given. Using this description an explicit formula for an arbitrary $6j$-symbol for the algebra $\mathfrak{gl}_n$ is derived. The $6j$-symbol is expressed through a value of a generalized hypergeometric function.
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